Knowledge graph question answering (KGQA) aims to answer natural language questions using knowledge graphs. Recent research leverages large language models (LLMs) to enhance KGQA reasoning, but faces limitations: retrieval-based methods are constrained by the quality of retrieved information, while agent-based methods rely heavily on proprietary LLMs. To address these limitations, we propose Retrieval-Judgment-Exploration (RJE), a framework that retrieves refined reasoning paths, evaluates their sufficiency, and conditionally explores additional evidence. Moreover, RJE introduces specialized auxiliary modules enabling small-sized LLMs to perform effectively: Reasoning Path Ranking, Question Decomposition, and Retriever-assisted Exploration. Experiments show that our approach with proprietary LLMs (such as GPT-4o-mini) outperforms existing baselines while enabling small open-source LLMs (such as 3B and 8B parameters) to achieve competitive results without fine-tuning LLMs. Additionally, RJE substantially reduces the number of LLM calls and token usage compared to agent-based methods, yielding significant efficiency improvements. Our code will be available at https://anonymous.4open.science/r/RJE-55CE.